A Search for Extraterrestrial Life (SETI), based on the possibility of interstellar communication via laser signals, is being designed to extend the search into the near-infrared spectral region (Wright et al, this conference). The dedicated near-infrared (900 to 1700 nm) instrument takes advantage of a new generation of avalanche photodiodes (APD), based on internal discrete amplification. These discrete APD (DAPD) detectors have a high speed response (< 1 GHz) and gain comparable to photomultiplier tubes, while also achieving significantly lower noise than previous APDs. We are investigating the use of DAPD detectors in this new astronomical instrument for a SETI search and transient source observations. We investigated experimentally the advantages of using a multiple detector device operating in parallel to remove spurious signals. We present the detector characterization and performance of the instrument in terms of false positive detection rates both theoretically and empirically through lab measurements. We discuss the required criteria that will be needed for laser light pulse detection in our experiment. These criteria are defined to optimize the trade between high detection efficiency and low false positive coincident signals, which can be produced by detector dark noise, background light, cosmic rays, and astronomical sources. We investigate experimentally how false coincidence rates depend on the number of detectors in parallel, and on the signal pulse height and width. We also look into the corresponding threshold to each of the signals to optimize the sensitivity while also reducing the false coincidence rates. Lastly, we discuss the analytical solution used to predict the probability of laser pulse detection with multiple detectors.